Without knowing which specific problems you're referring to, mathematicians are constantly cracking long-standing conjectures and proofs - stuff like problems in number theory, geometry, or topology that have stumped people for decades. The reason it matters is that solving these problems usually opens up entirely new ways of thinking about math, which eventually trickles down into practical applications like cryptography, computer algorithms, or physics models that actually do affect everyday life. Most people won't notice directly, but these breakthroughs are like removing roadblocks that let engineers and scientists build better things down the line. If you can point me to which award or problem you're asking about, I could give you more specific details - there's been quite a bit of news in this area over the past few years.